Thank you all for your insights and advice. As it happens, that KE flight arrives at 12:00, not 12:30, giving me another half hour.
Turns out, the UA 2:31 departure is the latest (UA) nonstop for the day.
mikew99, never fear! I did have a backup plan. Walk out of KE F and buy a ticket on Frontier leaving at 6:55. What the heck, I will have started the day flying MIAT out of ULN. Frontier would be a perfect bookend to the day.